ENGSCI 712 HAR Assignment¶

Introduction¶

This experiment aims to classify walking and running activites by extracting relevant features from time-series data, and fitting a Random Forest Classifier to these features.

Experiment¶

The linear acceleration in the x, y and z directions and the total acceleration of the subject was recorded using the 'Physics Toolbox' app on an iPhone 15 Pro.

The experiment was conducted over 6 different speeds on a treadmill, and were labelled as either walking or running:

  • Walking: 2 km/h, 3 km/h, 4 km/h.
  • Running: 8 km/h, 10 km/h, 12 km/h.

Each sample was recorded over approximately three minutes, with the iPhone held in the subject’s right hand. A standard running technique was used, with the arms positioned roughly perpendicular to the ground, swinging back and forth. Similarly, the walking technique followed a typical form, with the arms relaxed by the sides and swinging naturally back and forth.

In [71]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import warnings
import pickle
from tsfresh.transformers import FeatureSelector
from tsfresh.feature_extraction import extract_features
from tsfresh.utilities.dataframe_functions import impute
from sklearn.ensemble import RandomForestClassifier
from sklearn.model_selection import cross_val_score, RepeatedKFold
from pathlib import Path

warnings.filterwarnings(action='ignore')

%matplotlib inline

Directory Paths¶

In [72]:
data_dir = Path('..') / 'data'
fig_dir = Path('..') / 'reports' / 'figures'
model_dir = Path('..') / 'models'

Loading the Raw Data¶

In [73]:
two_kmph_df = pd.read_csv('../data/raw/acceleration-2kmph-walking.csv', index_col='time')
three_kmph_df = pd.read_csv('../data/raw/acceleration-3kmph-walking.csv', index_col='time')
four_kmph_df = pd.read_csv('../data/raw/acceleration-4kmph-walking.csv', index_col='time')
eight_kmph_df = pd.read_csv('../data/raw/acceleration-8kmph-running.csv', index_col='time')
ten_kmph_df = pd.read_csv('../data/raw/acceleration-10kmph-running.csv', index_col='time')
twelve_kmph_df = pd.read_csv('../data/raw/acceleration-12kmph-running.csv', index_col='time')
In [74]:
two_kmph_df.head()
Out[74]:
ax ay az atotal
time
0.00 0.22 -0.54 0.48 0.75
0.01 -0.07 -0.72 0.23 0.76
0.02 -0.46 -0.75 -0.32 0.94
0.03 -0.77 -0.61 -0.47 1.09
0.04 -0.79 -0.44 -0.36 0.97

Visualisation of Raw Data¶

Comparison of acceleration in the x-direction¶

In [75]:
all_speeds = [two_kmph_df, three_kmph_df, four_kmph_df, eight_kmph_df, ten_kmph_df, twelve_kmph_df] # List of all samples.
all_names = ['2_kmph', '3_kmph', '4_kmph', '8_kmph', '10_kmph', '12_kmph']
column_labels = two_kmph_df.columns

fig_ax, ax_x = plt.subplots(6, sharex=True)
fig_ax.set_figwidth(12)
fig_ax.set_figheight(22)

for i in range(len(ax_x)):
    ax_x[i].set_title(f'{all_names[i]}_ax')
    ax_x[i].set_xlabel('Time/s')
    ax_x[i].set_ylabel('Acceleration/ms-2')
    ax_x[i].plot(all_speeds[i].index, all_speeds[i]['ax'])

plt.savefig(fig_dir / 'ax_raw_fig.png')
plt.show()
No description has been provided for this image

Comparison of acceleration in the y-direction¶

In [76]:
fig_ay, ax_y = plt.subplots(6, sharex=True)
fig_ay.set_figwidth(12)
fig_ay.set_figheight(22)

for i in range(len(ax_y)):
    ax_y[i].set_title(f'{all_names[i]}_ay')
    ax_y[i].set_xlabel('Time/s')
    ax_y[i].set_ylabel('Acceleration/ms-2')
    ax_y[i].plot(all_speeds[i].index, all_speeds[i]['ay'])
    
plt.savefig(fig_dir / 'ay_raw_fig.png')
plt.show()
No description has been provided for this image

Comparison of acceleration in the z-direction¶

In [77]:
fig_az, ax_z = plt.subplots(6, sharex=True)
fig_az.set_figwidth(12)
fig_az.set_figheight(22)

for i in range(len(ax_z)):
    ax_z[i].set_title(f'{all_names[i]}_az')
    ax_z[i].set_xlabel('Time/s')
    ax_z[i].set_ylabel('Acceleration/ms-2')
    ax_z[i].plot(all_speeds[i].index, all_speeds[i]['az'])
        
plt.savefig(fig_dir / 'az_raw_fig.png')
plt.show()
No description has been provided for this image

Comparison of total acceleration¶

In [78]:
fig_atotal, ax_total = plt.subplots(6, sharex=True)
fig_atotal.set_figwidth(12)
fig_atotal.set_figheight(22)

for i in range(len(ax_total)):
    ax_total[i].set_title(f'{all_names[i]}_atotal')
    ax_total[i].set_xlabel('Time/s')
    ax_total[i].set_ylabel('Acceleration/ms-2')
    ax_total[i].plot(all_speeds[i].index, all_speeds[i]['atotal'])

plt.savefig(fig_dir / 'atotal_raw_fig.png')
plt.show()
No description has been provided for this image

Observations¶

There is a general increase in the amplitude and frequency of the signals as the speed of the activity increases. This is expected because a faster walk/run would result in faster swinging of the arms.

The duration of each sample was defined by noticeable spikes in signal amplitude at both the beginning and end, particularly in the z-direction. These sudden movements were intentionally introduced at the start and end of each walking or running activity to clearly mark the sample boundaries.

Preprocessing¶

The raw data time column was already formatted as a 'delta_t" column so creating this column was not necessary.

Removal of transition periods¶

The transitions periods were found by searching through the dataframes, and removing the outlier observations at the start and end.

In [79]:
pruned_two_kmph_df = two_kmph_df[(two_kmph_df.index >= 1.949) & (two_kmph_df.index <= 166.494)] # Pruning
pruned_two_kmph_df.index -= pruned_two_kmph_df.index[0] # Resetting index to start at time = 0.000
pruned_two_kmph_df
Out[79]:
ax ay az atotal
time
0.000 6.04 0.33 1.03 6.14
0.010 5.76 -0.20 0.97 5.84
0.020 5.57 -0.44 1.10 5.69
0.030 5.37 -0.93 0.93 5.53
0.040 5.07 -1.66 0.79 5.39
... ... ... ... ...
164.505 4.82 -1.04 1.53 5.17
164.515 4.89 -1.50 1.84 5.44
164.525 5.22 -2.11 1.97 5.97
164.535 5.60 -2.39 2.15 6.45
164.545 5.92 -2.66 2.41 6.92

16463 rows × 4 columns

In [80]:
pruned_three_kmph_df = three_kmph_df[(three_kmph_df.index >= 0.880) & (three_kmph_df.index <= 178.542)]
pruned_three_kmph_df.index -= pruned_three_kmph_df.index[0]
pruned_three_kmph_df
Out[80]:
ax ay az atotal
time
0.000 4.10 3.34 2.50 5.85
0.010 4.29 4.09 1.73 6.18
0.020 4.37 4.65 0.98 6.45
0.030 4.46 4.88 0.11 6.61
0.040 4.33 4.84 -0.59 6.52
... ... ... ... ...
177.622 5.02 0.21 1.00 5.12
177.632 5.08 0.04 1.24 5.23
177.642 5.34 -0.71 1.61 5.62
177.652 5.59 -1.35 2.02 6.09
177.662 6.18 -2.02 2.77 7.07

17772 rows × 4 columns

In [81]:
pruned_four_kmph_df = four_kmph_df[(four_kmph_df.index >= 1.590) & (four_kmph_df.index <= 178.856)]
pruned_four_kmph_df.index -= pruned_four_kmph_df.index[0]
pruned_four_kmph_df
Out[81]:
ax ay az atotal
time
0.000 -5.37 -7.04 -2.20 9.13
0.009 -4.03 -6.25 -1.15 7.52
0.020 -2.37 -5.30 0.06 5.81
0.029 -1.08 -4.49 1.06 4.74
0.040 -0.99 -4.37 1.20 4.64
... ... ... ... ...
177.226 7.05 3.15 1.12 7.80
177.236 7.09 3.13 1.33 7.86
177.247 7.18 3.07 1.55 7.96
177.256 7.42 3.08 1.94 8.26
177.266 7.77 3.13 2.50 8.74

17733 rows × 4 columns

In [82]:
pruned_eight_kmph_df = eight_kmph_df[(eight_kmph_df.index >= 0.710) & (eight_kmph_df.index <= 178.635)]
pruned_eight_kmph_df.index -= pruned_eight_kmph_df.index[0]
pruned_eight_kmph_df
Out[82]:
ax ay az atotal
time
0.000 3.40 4.45 8.10 9.85
0.010 1.73 4.43 4.86 6.79
0.020 0.35 4.27 2.24 4.83
0.030 -0.13 3.88 0.81 3.96
0.040 0.36 3.48 0.15 3.50
... ... ... ... ...
177.885 0.17 -0.11 -1.88 1.89
177.895 -0.76 2.07 3.42 4.07
177.905 -2.55 4.68 5.79 7.87
177.915 -4.01 7.83 6.26 10.79
177.925 -4.73 10.97 7.02 13.86

17799 rows × 4 columns

In [83]:
pruned_ten_kmph_df = ten_kmph_df[(ten_kmph_df.index >= 0.380) & (ten_kmph_df.index <= 179.094)]
pruned_ten_kmph_df.index -= pruned_ten_kmph_df.index[0]
pruned_ten_kmph_df
Out[83]:
ax ay az atotal
time
0.000 4.82 2.04 10.23 11.49
0.010 3.50 1.42 7.48 8.38
0.020 2.37 0.49 4.54 5.15
0.030 1.47 -0.80 2.18 2.75
0.040 1.17 -1.40 1.19 2.18
... ... ... ... ...
178.674 -8.75 -2.17 -0.78 9.04
178.684 -9.40 -0.62 -0.03 9.42
178.694 -10.02 1.27 1.31 10.18
178.704 -9.89 4.08 3.96 11.41
178.714 -6.29 7.13 8.02 12.44

17878 rows × 4 columns

In [84]:
pruned_twelve_kmph_df = twelve_kmph_df[(twelve_kmph_df.index >= 0.580) & (twelve_kmph_df.index <= 179.242)]
pruned_twelve_kmph_df.index -= pruned_twelve_kmph_df.index[0] # Reset index.
pruned_twelve_kmph_df
Out[84]:
ax ay az atotal
time
0.000 11.49 5.63 19.67 23.46
0.010 9.19 3.58 15.33 18.23
0.020 7.17 2.00 10.68 13.02
0.030 5.54 0.32 7.13 9.04
0.040 3.96 -1.35 4.88 6.43
... ... ... ... ...
178.622 -6.79 2.00 0.80 7.12
178.632 -6.79 2.23 1.78 7.37
178.642 -6.68 3.70 3.64 8.46
178.652 -4.83 6.53 7.26 10.90
178.662 1.25 10.46 14.18 17.67

17873 rows × 4 columns

Accelerations in the x-direction after pruning¶

In [85]:
all_speeds_pruned = [pruned_two_kmph_df, pruned_three_kmph_df, pruned_four_kmph_df, pruned_eight_kmph_df, pruned_ten_kmph_df, pruned_twelve_kmph_df]

fig_ax_pruned, ax_x_pruned = plt.subplots(6, sharex=True)
fig_ax_pruned.set_figwidth(12)
fig_ax_pruned.set_figheight(22)

for i in range(len(ax_x)):
    ax_x_pruned[i].set_title(f'{all_names[i]}_ax')
    ax_x_pruned[i].set_xlabel('Time/s')
    ax_x_pruned[i].set_ylabel('Acceleration/ms-2')
    ax_x_pruned[i].plot(all_speeds_pruned[i].index, all_speeds_pruned[i]['ax'])

plt.savefig(fig_dir / 'ax_pruned_fig.png')
plt.show()
No description has been provided for this image

Accelerations in the y-direction after pruning¶

In [86]:
fig_ay_pruned, ax_y_pruned = plt.subplots(6, sharex=True)
fig_ay_pruned.set_figwidth(12)
fig_ay_pruned.set_figheight(22)

for i in range(len(ax_x)):
    ax_y_pruned[i].set_title(f'{all_names[i]}_ay')
    ax_y_pruned[i].set_xlabel('Time/s')
    ax_y_pruned[i].set_ylabel('Acceleration/ms-2')
    ax_y_pruned[i].plot(all_speeds_pruned[i].index, all_speeds_pruned[i]['ay'])

plt.savefig(fig_dir / 'ay_pruned_fig.png')
plt.show()
No description has been provided for this image

Accelerations in the z-direction after pruning¶

In [87]:
fig_az_pruned, ax_z_pruned = plt.subplots(6, sharex=True)
fig_az_pruned.set_figwidth(12)
fig_az_pruned.set_figheight(22)

for i in range(len(ax_x)):
    ax_z_pruned[i].set_title(f'{all_names[i]}_az')
    ax_z_pruned[i].set_xlabel('Time/s')
    ax_z_pruned[i].set_ylabel('Acceleration/ms-2')
    ax_z_pruned[i].plot(all_speeds_pruned[i].index, all_speeds_pruned[i]['az'])

plt.savefig(fig_dir / 'az_pruned_fig.png')
plt.show()
No description has been provided for this image

Total Accelerations after pruning¶

In [88]:
fig_atotal_pruned, ax_total_pruned = plt.subplots(6, sharex=True)
fig_atotal_pruned.set_figwidth(12)
fig_atotal_pruned.set_figheight(22)

for i in range(len(ax_x)):
    ax_total_pruned[i].set_title(f'{all_names[i]}_atotal')
    ax_total_pruned[i].set_xlabel('Time/s')
    ax_total_pruned[i].set_ylabel('Acceleration/ms-2')
    ax_total_pruned[i].plot(all_speeds_pruned[i].index, all_speeds_pruned[i]['atotal'])

plt.savefig(fig_dir / 'atotal_pruned_fig.png')
plt.show()
No description has been provided for this image
In [89]:
for i in range(len(all_speeds_pruned)):
    print(f'{all_names[i]} signal length in seconds: {len(all_speeds_pruned[i]) / 100}')

2_kmph signal length in seconds: 164.63
3_kmph signal length in seconds: 177.72
4_kmph signal length in seconds: 177.33
8_kmph signal length in seconds: 177.99
10_kmph signal length in seconds: 178.78
12_kmph signal length in seconds: 178.73

The lengths of each signal are approximately equivalent, so there shouldn't be any concerns with an unbalanced dataset.

Extraction of Features¶

Window Indexing¶

'w' will represent walking, and 'r' will represent running in the window indices.

In [90]:
# Creating window indices.
idx_two = np.asarray(np.floor(pruned_two_kmph_df.reset_index().index / 100).values, int)
idx_three = np.asarray(np.floor(pruned_three_kmph_df.reset_index().index / 100).values + idx_two[-1] + 1, int)
idx_four = np.asarray(np.floor(pruned_four_kmph_df.reset_index().index / 100).values + idx_three[-1] + 1, int)

# Prefixing with 'w' which stands for walking. 
pruned_two_kmph_df['window_idx'] = ["w{:03}".format(i) for i in idx_two]
pruned_three_kmph_df['window_idx'] = ["w{:03}".format(i) for i in idx_three]
pruned_four_kmph_df['window_idx'] = ["w{:03}".format(i) for i in idx_four]

pruned_two_kmph_df.to_csv(data_dir / "interim" / "pruned_two_kmph.csv", index=False)
pruned_three_kmph_df.to_csv(data_dir / "interim" / "pruned_three_kmph.csv", index=False)
pruned_four_kmph_df.to_csv(data_dir / "interim" / "pruned_four_kmph.csv", index=False)

pruned_two_kmph_df
Out[90]:
ax ay az atotal window_idx
time
0.000 6.04 0.33 1.03 6.14 w000
0.010 5.76 -0.20 0.97 5.84 w000
0.020 5.57 -0.44 1.10 5.69 w000
0.030 5.37 -0.93 0.93 5.53 w000
0.040 5.07 -1.66 0.79 5.39 w000
... ... ... ... ... ...
164.505 4.82 -1.04 1.53 5.17 w164
164.515 4.89 -1.50 1.84 5.44 w164
164.525 5.22 -2.11 1.97 5.97 w164
164.535 5.60 -2.39 2.15 6.45 w164
164.545 5.92 -2.66 2.41 6.92 w164

16463 rows × 5 columns

In [91]:
idx_eight = np.asarray(np.floor(pruned_eight_kmph_df.reset_index().index / 100).values, int)
idx_ten = np.asarray(np.floor(pruned_ten_kmph_df.reset_index().index / 100).values + idx_eight[-1] + 1, int)
idx_twelve = np.asarray(np.floor(pruned_twelve_kmph_df.reset_index().index  / 100).values + idx_ten[-1] + 1, int)

# Prepend 'r' to window_idx to represent running..
pruned_eight_kmph_df['window_idx'] = ["r{:03}".format(i) for i in idx_eight]
pruned_ten_kmph_df['window_idx'] = ["r{:03}".format(i) for i in idx_ten]
pruned_twelve_kmph_df['window_idx'] = ["r{:03}".format(i) for i in idx_twelve]

pruned_eight_kmph_df.to_csv(data_dir / "interim" / "pruned_eight_kmph.csv", index=False)
pruned_ten_kmph_df.to_csv(data_dir / "interim" / "pruned_ten_kmph.csv", index=False)
pruned_twelve_kmph_df.to_csv(data_dir / "interim" / "pruned_twelve_kmph.csv", index=False)

pruned_eight_kmph_df
Out[91]:
ax ay az atotal window_idx
time
0.000 3.40 4.45 8.10 9.85 r000
0.010 1.73 4.43 4.86 6.79 r000
0.020 0.35 4.27 2.24 4.83 r000
0.030 -0.13 3.88 0.81 3.96 r000
0.040 0.36 3.48 0.15 3.50 r000
... ... ... ... ... ...
177.885 0.17 -0.11 -1.88 1.89 r177
177.895 -0.76 2.07 3.42 4.07 r177
177.905 -2.55 4.68 5.79 7.87 r177
177.915 -4.01 7.83 6.26 10.79 r177
177.925 -4.73 10.97 7.02 13.86 r177

17799 rows × 5 columns

Concatenating dataframes¶

In [92]:
walking_df = pd.concat([pruned_two_kmph_df, pruned_three_kmph_df, pruned_four_kmph_df])
walking_df.to_csv(data_dir / "interim" / "walking.csv", index=False)
walking_df
Out[92]:
ax ay az atotal window_idx
time
0.000 6.04 0.33 1.03 6.14 w000
0.010 5.76 -0.20 0.97 5.84 w000
0.020 5.57 -0.44 1.10 5.69 w000
0.030 5.37 -0.93 0.93 5.53 w000
0.040 5.07 -1.66 0.79 5.39 w000
... ... ... ... ... ...
177.226 7.05 3.15 1.12 7.80 w520
177.236 7.09 3.13 1.33 7.86 w520
177.247 7.18 3.07 1.55 7.96 w520
177.256 7.42 3.08 1.94 8.26 w520
177.266 7.77 3.13 2.50 8.74 w520

51968 rows × 5 columns

In [93]:
running_df = pd.concat([pruned_eight_kmph_df, pruned_ten_kmph_df, pruned_twelve_kmph_df])
running_df.to_csv(data_dir / "interim" / "running.csv", index=False)
running_df
Out[93]:
ax ay az atotal window_idx
time
0.000 3.40 4.45 8.10 9.85 r000
0.010 1.73 4.43 4.86 6.79 r000
0.020 0.35 4.27 2.24 4.83 r000
0.030 -0.13 3.88 0.81 3.96 r000
0.040 0.36 3.48 0.15 3.50 r000
... ... ... ... ... ...
178.622 -6.79 2.00 0.80 7.12 r535
178.632 -6.79 2.23 1.78 7.37 r535
178.642 -6.68 3.70 3.64 8.46 r535
178.652 -4.83 6.53 7.26 10.90 r535
178.662 1.25 10.46 14.18 17.67 r535

53550 rows × 5 columns

There are 51968 rows combined in the walking dataframe, and 53550 rows combined in the running dataframe.

In [94]:
walking_running_df = pd.concat([walking_df, running_df])
walking_running_df.to_csv(data_dir / "interim" / "walking_running.csv", index=False)
walking_running_df
Out[94]:
ax ay az atotal window_idx
time
0.000 6.04 0.33 1.03 6.14 w000
0.010 5.76 -0.20 0.97 5.84 w000
0.020 5.57 -0.44 1.10 5.69 w000
0.030 5.37 -0.93 0.93 5.53 w000
0.040 5.07 -1.66 0.79 5.39 w000
... ... ... ... ... ...
178.622 -6.79 2.00 0.80 7.12 r535
178.632 -6.79 2.23 1.78 7.37 r535
178.642 -6.68 3.70 3.64 8.46 r535
178.652 -4.83 6.53 7.26 10.90 r535
178.662 1.25 10.46 14.18 17.67 r535

105518 rows × 5 columns

The combined walking and running dataframes have 105518 rows in total.

In [95]:
walking_running_df['window_idx'].nunique()
Out[95]:
1057

There are 1057 unique window indices.

Extraction of Features¶

In [96]:
extracted_features = extract_features(walking_running_df, column_id='window_idx')

Feature Extraction: 100%|██████████| 20/20 [02:04<00:00,  6.23s/it]
In [114]:
impute(extracted_features) # Impute NA/null values.
extracted_features.to_csv(data_dir / "interim" / "extracted_features.csv", index=False)
extracted_features
Out[114]:
ax__variance_larger_than_standard_deviation ax__has_duplicate_max ax__has_duplicate_min ax__has_duplicate ax__sum_values ax__abs_energy ax__mean_abs_change ax__mean_change ax__mean_second_derivative_central ax__median ... atotal__fourier_entropy__bins_5 atotal__fourier_entropy__bins_10 atotal__fourier_entropy__bins_100 atotal__permutation_entropy__dimension_3__tau_1 atotal__permutation_entropy__dimension_4__tau_1 atotal__permutation_entropy__dimension_5__tau_1 atotal__permutation_entropy__dimension_6__tau_1 atotal__permutation_entropy__dimension_7__tau_1 atotal__query_similarity_count__query_None__threshold_0.0 atotal__mean_n_absolute_max__number_of_maxima_7
r000 1.0 0.0 0.0 1.0 86.13 1655.8011 0.681111 0.039495 0.006633 -0.075 ... 0.575228 0.706253 1.283294 1.374172 2.122390 2.857326 3.476007 3.990108 0.0 12.088571
r001 1.0 0.0 0.0 1.0 -66.64 5067.8256 1.277879 -0.083131 0.016633 -2.755 ... 0.369812 0.508382 1.266372 1.165692 1.682566 2.242483 2.781797 3.209318 0.0 23.260000
r002 1.0 0.0 0.0 1.0 72.64 2051.5922 0.859192 0.020808 -0.011020 0.115 ... 0.481199 0.668811 1.103096 1.144288 1.580317 2.029087 2.486393 2.894001 0.0 15.138571
r003 1.0 0.0 0.0 1.0 1.78 1935.8234 0.776869 0.003535 0.003214 -0.855 ... 0.413917 0.508382 1.318528 1.168784 1.649243 2.143991 2.615653 3.061648 0.0 15.002857
r004 1.0 0.0 0.0 1.0 70.12 2665.7300 0.916970 -0.037980 -0.003929 -0.940 ... 0.464277 0.518641 0.919223 1.116646 1.566289 1.959137 2.364171 2.763991 0.0 16.927143
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
w516 1.0 1.0 0.0 1.0 24.00 2248.3118 0.261414 0.059394 0.000816 -0.530 ... 0.288342 0.288342 0.760618 0.937191 1.231097 1.485550 1.736844 2.003761 0.0 8.751429
w517 1.0 0.0 0.0 1.0 -58.68 1452.6522 0.245455 0.040808 0.003776 -1.650 ... 0.165443 0.165443 0.695993 1.115882 1.539055 1.953655 2.340578 2.683975 0.0 7.587143
w518 1.0 0.0 0.0 1.0 -27.39 1695.3341 0.216364 -0.085051 0.000765 -1.705 ... 0.288342 0.288342 0.545824 1.095106 1.520087 1.927013 2.302943 2.600988 0.0 8.987143
w519 1.0 0.0 0.0 1.0 93.73 2043.0013 0.261414 -0.022020 -0.002653 1.225 ... 0.288342 0.288342 0.695993 1.194533 1.743452 2.231419 2.698119 3.120640 0.0 7.332857
w520 1.0 0.0 0.0 1.0 85.86 586.0924 0.308750 0.290625 0.002097 2.210 ... 0.443757 0.659872 0.871781 0.919907 1.216203 1.381154 1.549826 1.669296 0.0 7.915714

1057 rows × 3132 columns

The resulting feature matrix has 1057 rows and 3132 columns. In other words, 3132 features have been extracted over 1057 windows.

Activity Recognition Model¶

Denote running as true and walking as false.

In [98]:
target = pd.Series(extracted_features.index.str[0] == 'r', index=extracted_features.index)
target
Out[98]:
r000     True
r001     True
r002     True
r003     True
r004     True
        ...  
w516    False
w517    False
w518    False
w519    False
w520    False
Length: 1057, dtype: bool

Feature Selection¶

In [99]:
select = FeatureSelector()
select.fit(extracted_features, target)
Out[99]:
FeatureSelector()
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
FeatureSelector()

Feature Reduction¶

In [100]:
select.transform(extracted_features)
Out[100]:
az__variance_larger_than_standard_deviation ax__number_crossing_m__m_-1 az__ratio_value_number_to_time_series_length az__absolute_maximum az__maximum ay__maximum atotal__maximum atotal__absolute_maximum az__quantile__q_0.8 az__quantile__q_0.1 ... atotal__cwt_coefficients__coeff_6__w_2__widths_(2, 5, 10, 20) ay__cwt_coefficients__coeff_8__w_2__widths_(2, 5, 10, 20) ay__cwt_coefficients__coeff_1__w_10__widths_(2, 5, 10, 20) atotal__fft_coefficient__attr_"angle"__coeff_17 atotal__change_quantiles__f_agg_"mean"__isabs_False__qh_1.0__ql_0.8 atotal__ar_coefficient__coeff_9__k_10 ax__friedrich_coefficients__coeff_0__m_3__r_30 az__fft_coefficient__attr_"angle"__coeff_43 ax__fft_coefficient__attr_"angle"__coeff_1 ay__has_duplicate_max
r000 1.0 6.0 0.940000 11.20 11.20 7.58 13.14 13.14 5.762 -3.880 ... -6.353659 -0.175893 1.941404 89.845029 0.065333 0.109936 -0.000966 -18.856243 9.153098 0.0
r001 1.0 7.0 0.990000 14.89 14.89 9.43 29.18 29.18 3.218 -3.976 ... 1.133600 0.410486 8.307796 -17.953434 -0.274706 -0.151449 -0.000304 -12.548361 153.895776 0.0
r002 1.0 5.0 0.950000 10.66 10.66 6.44 17.33 17.33 5.576 -4.829 ... 0.461592 4.009567 7.893092 17.612480 0.116250 0.937414 0.000122 116.239548 -38.470514 0.0
r003 1.0 6.0 0.970000 10.30 10.30 6.49 16.28 16.28 2.810 -5.117 ... 1.495860 -0.861225 -7.231616 145.591365 0.087500 -0.031573 -0.001296 -5.472196 -143.192616 0.0
r004 1.0 5.0 0.960000 12.20 12.20 8.19 19.07 19.07 6.310 -4.689 ... -1.133400 2.478037 -3.543754 17.552563 -0.113125 -0.041570 -0.000166 127.388472 33.136497 0.0
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
w516 0.0 1.0 0.840000 2.00 1.57 4.31 9.03 9.03 1.060 -1.020 ... 0.412208 -0.172704 0.078933 140.826072 -0.010000 0.127181 -0.000585 -8.058655 81.531072 0.0
w517 0.0 2.0 0.880000 2.35 2.35 1.36 8.35 8.35 1.244 -0.946 ... 0.155062 -0.711380 3.854368 101.681248 0.090556 0.137142 0.000878 159.152159 18.323403 0.0
w518 0.0 2.0 0.810000 1.64 1.64 3.64 9.24 9.24 0.896 -0.740 ... 1.370432 0.728550 2.459767 -58.089717 -0.118333 0.367404 0.000721 -4.611620 -46.002433 0.0
w519 0.0 1.0 0.720000 2.32 1.86 3.75 7.51 7.51 1.010 -0.250 ... 0.023910 1.001787 -2.684173 89.093543 -0.020000 0.121748 -0.000866 -10.821067 -92.594920 0.0
w520 0.0 1.0 0.939394 2.50 2.50 3.15 8.74 8.74 0.900 -0.796 ... 1.611997 -0.235135 -7.203606 -0.722175 0.260000 0.647203 -0.000445 1.482437 90.135916 0.0

1057 rows × 1202 columns

In [101]:
p_values_top5 = select.p_values[:5]
p_values_top5
Out[101]:
array([5.00047690e-238, 2.38755945e-177, 2.74217433e-174, 3.20327653e-174,
       3.20534176e-174])
In [102]:
relevant_features_top5 = select.relevant_features[:5]
relevant_features_top5
Out[102]:
['az__variance_larger_than_standard_deviation',
 'ax__number_crossing_m__m_-1',
 'az__ratio_value_number_to_time_series_length',
 'az__absolute_maximum',
 'az__maximum']

5 Features with the smallest p-values¶

In [103]:
relevant_feats_p_value_top5 = pd.DataFrame({"Feature": relevant_features_top5, "p-values": p_values_top5})
relevant_feats_p_value_top5.to_csv(data_dir / "interim" / "relevant_feats_p_value_top5.csv", index=False)
relevant_feats_p_value_top5
Out[103]:
Feature p-values
0 az__variance_larger_than_standard_deviation 5.000477e-238
1 ax__number_crossing_m__m_-1 2.387559e-177
2 az__ratio_value_number_to_time_series_length 2.742174e-174
3 az__absolute_maximum 3.203277e-174
4 az__maximum 3.205342e-174
In [ ]:
relevant_features_top5_df = pd.concat([extracted_features[relevant_features_top5], pd.DataFrame(target, columns=["target"])], axis=1)
relevant_features_top5_df
Out[ ]:
az__variance_larger_than_standard_deviation ax__number_crossing_m__m_-1 az__ratio_value_number_to_time_series_length az__absolute_maximum az__maximum target
r000 1.0 6.0 0.940000 11.20 11.20 True
r001 1.0 7.0 0.990000 14.89 14.89 True
r002 1.0 5.0 0.950000 10.66 10.66 True
r003 1.0 6.0 0.970000 10.30 10.30 True
r004 1.0 5.0 0.960000 12.20 12.20 True
... ... ... ... ... ... ...
w516 0.0 1.0 0.840000 2.00 1.57 False
w517 0.0 2.0 0.880000 2.35 2.35 False
w518 0.0 2.0 0.810000 1.64 1.64 False
w519 0.0 1.0 0.720000 2.32 1.86 False
w520 0.0 1.0 0.939394 2.50 2.50 False

1057 rows × 6 columns

Visualisation of the 5 Features with the smallest p-value¶

In [105]:
sns.pairplot(relevant_features_top5_df, hue='target')
plt.savefig(fig_dir / 'five_smallest_p_value_pairplot_fig.png')
plt.show()
No description has been provided for this image

The distributions on the diagonal entries of the figure show that these features are good choices for classifying between walking and running due to the lack of overlap. This is further supported by the scatter plots, which also illustrate little to no overlap

In [106]:
all_relevant_features_df = extracted_features[select.relevant_features]
all_relevant_features_df.to_csv(data_dir / "interim" / "all_relevant_features.csv", index=False)
all_relevant_features_df
Out[106]:
az__variance_larger_than_standard_deviation ax__number_crossing_m__m_-1 az__ratio_value_number_to_time_series_length az__absolute_maximum az__maximum ay__maximum atotal__maximum atotal__absolute_maximum az__quantile__q_0.8 az__quantile__q_0.1 ... atotal__cwt_coefficients__coeff_6__w_2__widths_(2, 5, 10, 20) ay__cwt_coefficients__coeff_8__w_2__widths_(2, 5, 10, 20) ay__cwt_coefficients__coeff_1__w_10__widths_(2, 5, 10, 20) atotal__fft_coefficient__attr_"angle"__coeff_17 atotal__change_quantiles__f_agg_"mean"__isabs_False__qh_1.0__ql_0.8 atotal__ar_coefficient__coeff_9__k_10 ax__friedrich_coefficients__coeff_0__m_3__r_30 az__fft_coefficient__attr_"angle"__coeff_43 ax__fft_coefficient__attr_"angle"__coeff_1 ay__has_duplicate_max
r000 1.0 6.0 0.940000 11.20 11.20 7.58 13.14 13.14 5.762 -3.880 ... -6.353659 -0.175893 1.941404 89.845029 0.065333 0.109936 -0.000966 -18.856243 9.153098 0.0
r001 1.0 7.0 0.990000 14.89 14.89 9.43 29.18 29.18 3.218 -3.976 ... 1.133600 0.410486 8.307796 -17.953434 -0.274706 -0.151449 -0.000304 -12.548361 153.895776 0.0
r002 1.0 5.0 0.950000 10.66 10.66 6.44 17.33 17.33 5.576 -4.829 ... 0.461592 4.009567 7.893092 17.612480 0.116250 0.937414 0.000122 116.239548 -38.470514 0.0
r003 1.0 6.0 0.970000 10.30 10.30 6.49 16.28 16.28 2.810 -5.117 ... 1.495860 -0.861225 -7.231616 145.591365 0.087500 -0.031573 -0.001296 -5.472196 -143.192616 0.0
r004 1.0 5.0 0.960000 12.20 12.20 8.19 19.07 19.07 6.310 -4.689 ... -1.133400 2.478037 -3.543754 17.552563 -0.113125 -0.041570 -0.000166 127.388472 33.136497 0.0
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
w516 0.0 1.0 0.840000 2.00 1.57 4.31 9.03 9.03 1.060 -1.020 ... 0.412208 -0.172704 0.078933 140.826072 -0.010000 0.127181 -0.000585 -8.058655 81.531072 0.0
w517 0.0 2.0 0.880000 2.35 2.35 1.36 8.35 8.35 1.244 -0.946 ... 0.155062 -0.711380 3.854368 101.681248 0.090556 0.137142 0.000878 159.152159 18.323403 0.0
w518 0.0 2.0 0.810000 1.64 1.64 3.64 9.24 9.24 0.896 -0.740 ... 1.370432 0.728550 2.459767 -58.089717 -0.118333 0.367404 0.000721 -4.611620 -46.002433 0.0
w519 0.0 1.0 0.720000 2.32 1.86 3.75 7.51 7.51 1.010 -0.250 ... 0.023910 1.001787 -2.684173 89.093543 -0.020000 0.121748 -0.000866 -10.821067 -92.594920 0.0
w520 0.0 1.0 0.939394 2.50 2.50 3.15 8.74 8.74 0.900 -0.796 ... 1.611997 -0.235135 -7.203606 -0.722175 0.260000 0.647203 -0.000445 1.482437 90.135916 0.0

1057 rows × 1202 columns

Fitting Random Forest Classifier and cross-validation¶

In [107]:
cv = RepeatedKFold(n_splits=10, n_repeats=10, random_state=42) # Perform 10-fold cv 10 times.

clf = RandomForestClassifier()
scores = cross_val_score(clf, all_relevant_features_df, target, cv=cv)
In [108]:
scores
Out[108]:
array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,
       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])

The scores array indicates that all 100 training and testing folds from the 10-times repeated 10-fold cross-validation achieved 100% prediction accuracy.

Fitting on all data¶

In [109]:
clf2 = RandomForestClassifier()
clf2.fit(all_relevant_features_df, target)

with open(model_dir / 'final_model.pkl','wb') as f:
    pickle.dump(clf, f)
In [110]:
importances = clf2.feature_importances_
feature_importance_df = pd.DataFrame({
    'Feature': all_relevant_features_df.columns,
    'Importance': importances
})

feature_importance_df
Out[110]:
Feature Importance
0 az__variance_larger_than_standard_deviation 0.00
1 ax__number_crossing_m__m_-1 0.00
2 az__ratio_value_number_to_time_series_length 0.00
3 az__absolute_maximum 0.03
4 az__maximum 0.00
... ... ...
1197 atotal__ar_coefficient__coeff_9__k_10 0.00
1198 ax__friedrich_coefficients__coeff_0__m_3__r_30 0.00
1199 az__fft_coefficient__attr_"angle"__coeff_43 0.00
1200 ax__fft_coefficient__attr_"angle"__coeff_1 0.00
1201 ay__has_duplicate_max 0.00

1202 rows × 2 columns

5 Most Important Features Identified by feature_importances_¶

In [111]:
feature_importance_sorted_df = feature_importance_df.sort_values(by='Importance', ascending=False)
feature_importance_sorted_df.to_csv(data_dir / "interim" / "feature_importance_sorted.csv", index=False)
feature_importance_sorted_df.head(5)
Out[111]:
Feature Importance
111 atotal__change_quantiles__f_agg_"var"__isabs_T... 0.07
65 ax__change_quantiles__f_agg_"var"__isabs_True_... 0.04
14 ax__change_quantiles__f_agg_"mean"__isabs_True... 0.03
27 atotal__change_quantiles__f_agg_"mean"__isabs_... 0.03
3 az__absolute_maximum 0.03

The 5 most important features:

  • change_quantiles (atotal, ax, ax, atotal): Finds points in the time series less than ql and greater than qh, and computes the difference between adjacent values (absolute diference if isabs=True) that fall outside this corridor, then aggregates using the function defined for the f_agg parameter.
  • maximum (az): The absolute maximum value of the time series.
In [112]:
all_relevant_features_with_labels = pd.concat([extracted_features[feature_importance_sorted_df['Feature'].iloc[:5]], pd.DataFrame(target, columns=['target'])], axis=1)
all_relevant_features_with_labels.to_csv(data_dir / "processed" / "all_relevant_features_with_labels.csv", index=False)
all_relevant_features_with_labels
Out[112]:
atotal__change_quantiles__f_agg_"var"__isabs_True__qh_0.8__ql_0.0 ax__change_quantiles__f_agg_"var"__isabs_True__qh_1.0__ql_0.0 ax__change_quantiles__f_agg_"mean"__isabs_True__qh_1.0__ql_0.0 atotal__change_quantiles__f_agg_"mean"__isabs_True__qh_0.6__ql_0.0 az__absolute_maximum target
r000 0.398618 0.255426 0.681111 0.812642 11.20 True
r001 0.913306 1.991750 1.277879 0.942778 14.89 True
r002 0.506248 0.774904 0.859192 0.862727 10.66 True
r003 0.497177 0.762527 0.776869 0.850545 10.30 True
r004 0.544153 0.565282 0.916970 0.819091 12.20 True
... ... ... ... ... ... ...
w516 0.047892 0.022006 0.261414 0.334737 2.00 False
w517 0.019968 0.021154 0.245455 0.209310 2.35 False
w518 0.018304 0.021092 0.216364 0.163860 1.64 False
w519 0.069663 0.049792 0.261414 0.291636 2.32 False
w520 0.038102 0.028880 0.308750 0.352105 2.50 False

1057 rows × 6 columns

In [113]:
sns.pairplot(all_relevant_features_with_labels, hue='target')
plt.savefig(fig_dir / 'five_most_important_feats_pairplot_fig.png')
plt.show()
No description has been provided for this image

When comparing the walking and running distributions, the difference is quite apparent. There is essentially no overlap between the two distributions on the diagonal entries, which makes these excellent features for classification. This is further supported by the scatter plots, which also show a clear separation between walking and running activities.